Vol. 56, No. 1, 1975

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ISSN: 0030-8730
Central embeddings in semi-simple rings

Shimshon A. Amitsur

Vol. 56 (1975), No. 1, 1–6
Abstract

A ring S is a central extension of a subring R if S = RC and C is the centralizer of R in S, i.e., C = {s S;sr = rs} for every r R. We shall also say that R is centrally embedded in

S.

We have shown that if a ring R is centrally embedded in a simple artinian ring then R is a prime Öre ring and its quotient ring Q is the minimal central extension of R which is a simple artinian ring; furthermore, the centralizer of R can be characterized. In the present note we extend these results and show that rings which can be centrally embedded in semi-simple artinian rings are semi-prime Öre rings with a finite number of minimal primes and their rings of quotients are the minimal central extension of this type.

Mathematical Subject Classification
Primary: 16A08
Milestones
Received: 28 December 1973
Published: 1 January 1975
Authors
Shimshon A. Amitsur